Question

A speaker emits sound waves with a frequency of 400 Hz. The sound waves travel through air with a speed of 343 m/s. Calculate the wavelength of these sound waves.

Answer

The wavelength of a sound wave is given by the formula:

λ = v/f

where λ is the wavelength, v is the velocity of the sound wave, and f is the frequency of the sound wave.

Given: Frequency (f) = 400 Hz Velocity (v) = 343 m/s

Substituting these values into the formula:

λ = 343 m/s / 400 Hz

To simplify the calculation, we can convert hertz (Hz) to per second (1/s):

1 Hz = 1/s

Therefore:

λ = 343 m/s / 400/s

To divide by a fraction, we can multiply by the reciprocal:

λ = 343 m/s * (1/400 s)

Simplifying the expression:

λ = 343/400 m

Further simplifying:

λ ≈ 0.857 m

Therefore, the wavelength of these sound waves is approximately 0.857 meters.